{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:EBPVJ3IH6TFSDUUI7JGT5C64LZ","short_pith_number":"pith:EBPVJ3IH","schema_version":"1.0","canonical_sha256":"205f54ed07f4cb21d288fa4d3e8bdc5e70d6171a8c96856013443dc37a48aa71","source":{"kind":"arxiv","id":"1905.03870","version":1},"attestation_state":"computed","paper":{"title":"Gradient methods exploiting spectral properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Hongchao Zhang, Xin-Wei Liu, Yakui Huang, Yu-Hong Dai","submitted_at":"2019-05-09T21:46:25Z","abstract_excerpt":"We propose a new stepsize for the gradient method. It is shown that this new stepsize will converge to the reciprocal of the largest eigenvalue of the Hessian, when Dai-Yang's asymptotic optimal gradient method (Computational Optimization and Applications, 2006, 33(1): 73-88) is applied for minimizing quadratic objective functions. Based on this spectral property, we develop a monotone gradient method that takes a certain number of steps using the asymptotically optimal stepsize by Dai and Yang, and then follows by some short steps associated with this new stepsize. By employing one step retar"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1905.03870","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-05-09T21:46:25Z","cross_cats_sorted":[],"title_canon_sha256":"fb8428776a87f9deccba8e1bc98b9a24a1c315f458688e6d862b4743b62109a0","abstract_canon_sha256":"b5202362112636a259c120ca5d81bf05064a4039aade291e9b68bcd9296c53af"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:35.347081Z","signature_b64":"HC33eKKyyHtqCFRxzaSIym3IwrdCcp/ibLNVF4gPUS+pAKK3o6DXo98iM6l7nRz4EDupCy628z8rQalFBD41Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"205f54ed07f4cb21d288fa4d3e8bdc5e70d6171a8c96856013443dc37a48aa71","last_reissued_at":"2026-05-17T23:46:35.346475Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:35.346475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gradient methods exploiting spectral properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Hongchao Zhang, Xin-Wei Liu, Yakui Huang, Yu-Hong Dai","submitted_at":"2019-05-09T21:46:25Z","abstract_excerpt":"We propose a new stepsize for the gradient method. It is shown that this new stepsize will converge to the reciprocal of the largest eigenvalue of the Hessian, when Dai-Yang's asymptotic optimal gradient method (Computational Optimization and Applications, 2006, 33(1): 73-88) is applied for minimizing quadratic objective functions. Based on this spectral property, we develop a monotone gradient method that takes a certain number of steps using the asymptotically optimal stepsize by Dai and Yang, and then follows by some short steps associated with this new stepsize. By employing one step retar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.03870","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1905.03870","created_at":"2026-05-17T23:46:35.346586+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.03870v1","created_at":"2026-05-17T23:46:35.346586+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.03870","created_at":"2026-05-17T23:46:35.346586+00:00"},{"alias_kind":"pith_short_12","alias_value":"EBPVJ3IH6TFS","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_16","alias_value":"EBPVJ3IH6TFSDUUI","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_8","alias_value":"EBPVJ3IH","created_at":"2026-05-18T12:33:15.570797+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EBPVJ3IH6TFSDUUI7JGT5C64LZ","json":"https://pith.science/pith/EBPVJ3IH6TFSDUUI7JGT5C64LZ.json","graph_json":"https://pith.science/api/pith-number/EBPVJ3IH6TFSDUUI7JGT5C64LZ/graph.json","events_json":"https://pith.science/api/pith-number/EBPVJ3IH6TFSDUUI7JGT5C64LZ/events.json","paper":"https://pith.science/paper/EBPVJ3IH"},"agent_actions":{"view_html":"https://pith.science/pith/EBPVJ3IH6TFSDUUI7JGT5C64LZ","download_json":"https://pith.science/pith/EBPVJ3IH6TFSDUUI7JGT5C64LZ.json","view_paper":"https://pith.science/paper/EBPVJ3IH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.03870&json=true","fetch_graph":"https://pith.science/api/pith-number/EBPVJ3IH6TFSDUUI7JGT5C64LZ/graph.json","fetch_events":"https://pith.science/api/pith-number/EBPVJ3IH6TFSDUUI7JGT5C64LZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EBPVJ3IH6TFSDUUI7JGT5C64LZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EBPVJ3IH6TFSDUUI7JGT5C64LZ/action/storage_attestation","attest_author":"https://pith.science/pith/EBPVJ3IH6TFSDUUI7JGT5C64LZ/action/author_attestation","sign_citation":"https://pith.science/pith/EBPVJ3IH6TFSDUUI7JGT5C64LZ/action/citation_signature","submit_replication":"https://pith.science/pith/EBPVJ3IH6TFSDUUI7JGT5C64LZ/action/replication_record"}},"created_at":"2026-05-17T23:46:35.346586+00:00","updated_at":"2026-05-17T23:46:35.346586+00:00"}